论文标题
动力系统和神经网络
Dynamical Systems and Neural Networks
论文作者
论文摘要
神经网络（NNS）已被确定为复杂动力系统研究的潜在强大工具。一个很好的例子是NN微分方程（DE）求解器，该方程式求解器为各种动力学系统的演变提供了封闭形式，可区分的功能近似值。这种NN求解器的主要缺点可能是获得与现有数值求解器相当的精确度所需的计算资源量。我们为现有动力系统提供新的策略，有效地利用了\ textit {Learning}信息，以加快其培训过程，同时仍采用完全无监督的方法。我们通过Koopman操作员理论（KOT）建立了NN理论与动力学系统理论之间的基本联系，该理论表明神经网的通常训练过程是确定多个Koopman感兴趣的操作员的肥沃基础。我们结束时阐明了KOT通常对NNS可能拥有的某些应用。
Neural Networks (NNs) have been identified as a potentially powerful tool in the study of complex dynamical systems. A good example is the NN differential equation (DE) solver, which provides closed form, differentiable, functional approximations for the evolution of a wide variety of dynamical systems. A major disadvantage of such NN solvers can be the amount of computational resources needed to achieve accuracy comparable to existing numerical solvers. We present new strategies for existing dynamical system NN DE solvers, making efficient use of the \textit{learnt} information, to speed up their training process, while still pursuing a completely unsupervised approach. We establish a fundamental connection between NN theory and dynamical systems theory via Koopman Operator Theory (KOT), by showing that the usual training processes for Neural Nets are fertile ground for identifying multiple Koopman operators of interest. We end by illuminating certain applications that KOT might have for NNs in general.
